Ideal Gas Law Lab

Chemistry 211 Lab Fall 2002

Lab #6 -- Practical Use of the Ideal Gas Law:

Identification of an Unknown Metal Sample

Purpose

The identification of a metal sample, chosen at random from three possibilities. The sample will be reacted with aqueous strong acid, which will result in the production of a gas. The gas sample is collected over water, and then quantified by applying the Ideal Gas Law. Comparison of reaction stoichiometry is then used to determine moles of unknown metal, and with the mass of the unknown sample, molar mass is obtained (g/mol), providing a basis for the identification of the unknown metal.

Introduction

The Ideal Gas Law is a staple of modern chemistry textbooks, and it inspires much fear and loathing amongst undergraduate students. One can speculate that the reason for this is the rote calculation involved in using the law, and not necessarily the law itself. The Ideal Gas Law takes advantage of a special set of physical conditions, called collectively standard temperature and pressure, or "STP" for short. Standard temperature is 273.15 K and standard pressure is 101,325 Pa.

Using SI units, one mole of any gas sample (regardless of formula or mass) collected at STP occupies a equally standard volume in liters. The modern, textbook version of the Ideal Gas Law is the result of a combination of several other laws concerning the properties of gases:

Boyle's Law: P x V = constant (at constant temperature, sample size), or

pressure and volume are inversely proportional

Charles' Law: V = constant x T (at constant pressure, sample size), or

volume and temperature are directly proportional

Avogadro's Law: V  n (at constant temperature, pressure), or

volume is proportional to the number of gas molecules

There is no direct, mathematically valid way to combine these laws into what is today called the Ideal Gas Law; but you should take a moment to notice how Boyle's Law, Charles' Law, and Avogadro's Law can be equally well expressed using the Ideal Gas Law.

Modern Ideal Gas Law: P V = n R T (valid at 'ordinary' pressures and temperatures), where

P = pressure, V = volume, T = temperature, n = moles of gas, and R = the Ideal Gas Law constant.

It is customary to measure these various quantities in SI units, or to convert measured values into SI units from other unit systems. When SI units are used*, R has the value 0.08206 L * atm / mol * K.

* NOTE: the SI unit of pressure is the Pascal (Pa). It is common, however, to use atmospheres (atm) as the pressure unit for gas law calculations, thereby requiring the memorization of only one value for R (1 atm = 101,325 Pa = 760 torr).

Design of the Experiment and Background Chemistry

A sample of an unknown metal will be allowed to react with aqueous hydrochloric acid (HCl). Hydrogen gas will be produced as one of the reaction products, and a water-soluble metal chloride salt will be the other product:

Unknown Metal #1 and #2: M(s) + 2HCl(aq) ----------> MCl2(aq) + H2(g)

Unknown Metal #3: 2M(s) + 6HCl(aq) ----------> 2MCl3(aq) + 3H2(g)

The unknown metal will dissolve as the reaction proceeds, and the gas produced will be collected over water and quantified by volume (mL). Using the Ideal Gas Law, the value n, number of moles of gas produced, can be determined, assuming the other variables are also measured. Take a moment to re-arrange the Ideal Gas Law to solve for n.

You will measure the atmospheric pressure in the lab the day you do the experiment (or, have that value provided by the Teaching Assistant or prep. room staff). It is unlikely they will be using a barometer that measures pressure in atmospheres, so expect to convert the recorded pressure to atmospheres from some other pressure unit. Your textbook should have the necessary tables to convert pressure to atmospheres from other commonly used pressure units.

Volume measurements will be in milliliters (mL). Again, this will need to be converted to a volume unit friendly to the value for R given in this text. Likewise, temperatures will need to be converted to Kelvin from degrees Celsius.

The objective, after each of three trials, will be to solve for n, moles of gas produced. Using the above stoichiometric relationships, the number of moles of metal consumed can be determined. Dividing grams of metal used by moles of metal gives the molar mass (g/mol) for the unknown metal.

One last thing to keep in mind: the gas being collected is not just hydrogen. Since it is being collected over water, the pressure of just the hydrogen gas inside the collection tube needs to be corrected for the presence of water vapor. Thus, the total pressure of the gas collected is dictated by Dalton's Law of Partial Pressures:

Ptot = P (H2) + P (H2O)

The vapor pressure of water needs to be subtracted from the total pressure. It is the pressure due to hydrogen gas alone that must be used to determine n, using the Ideal Gas Law. The vapor pressure of water at various temperatures can be found in a variety of reference books, including the 211 lecture text. Values not precisely stated (e.g., the 23.1oC in the sample data) in such tables can be reasonably interpolated from the two available values above and below the determined temperature of the collected water vapor:

Vapor pressure of water, 23oC: 21.07 torr

Vapor pressure of water, 24oC: 22.38 torr

Difference: 1.31 torr

Difference x (0.1): 0.131 torr

Interpolated vapor pressure of water (v.p. @ 23oC + difference x (0.1)): 21.07 + 0.131 = 21.20 torr

Sample Data and Calculations

Sample of an unknown metal, following #1 or #2 stoichiometry: 0.111 g

Volume